An open-plus-closed-loop approach to synchronization of chaotic and hyperchaotic maps

In this paper, the open-plus-closed-loop control strategy is adapted to synchronize discrete chaos. Two synchronization problems of chaos are studied: one is to drive a chaotic map with the aim of obtaining desirable chaotic dynamics; the other is to identify chaotic behaviors of a nonlinear map for different initial conditions. It is shown that in the latter case the needed control signal can be arbitrarily small. Two numerical examples, namely, the Gaussian map and a hyperchaotic map, are investigated in detail for demonstration of the effectiveness of the approach. The results show that synchronization of discrete chaos can be realized if the control is activated in the basin of entrainment.